How to replace a variable or function with another variable or function ?

for example. I have a function

y = x*(x^2 - 1)

In this function, I want to replace x with cos(t)

the required function is,

y = cos(t) ( (cos(t))^2 - 1)

Answer 1

[Are Mjaavatten]

You could define an anonymous function f(x):

 f = @(x) x.*(x.^2-1);

Note the '.' before the * and ^operators. This lets the function work with array inputs. I use this feature in the example at the end.

Now you can use cos(t) as an argument to f:

 t = 2;
 y = f(cos(t))

Or you may define a new anonymous function g:

 g = @(t) f(cos(t));

You may now try something like this:

 t = linspace(0,2*pi);
 plot(t,g(t))

You may want to take a look at the Matlab documentation for anonymous functions.

[Pavan Bharadwaj]

Thank you for your answer.

In the case I am working on, The result of the differential acts the function and in this function I want to replace x by cos(t). The resultant function has to again be differentiated with respect to t.

Cheers, Pavan

[Are Mjaavatten]

Pavan,

It seems from your comment that I may have misunderstood your question.

You mention 'differential' in your comment. Are you asking how to do some symbolic manipulations to the equations to yield a mathemathical differential (e.g. dy or dx), formulate a differential equation, or maybe how to find the derivative dy/dt?

If so, maybe the symbolic math toolbox may be of help. I do not have this toolbox, but if you state your problem more clearly, maybe someone else can give a relevant answer.

Answer 2

[Steven Lord]

Since it seems like you want to perform symbolic computations, see the subs function in Symbolic Math Toolbox.

Answer 3

[Parth Shrimali]

syms x y z;

p = 3*x + y +z;

% suppose you wanna replace 'x' with

% new variable 'a' in our difined

% variable 'p'

syms a;

subs(p,'x',a)